-д хадгалсан:
| Үндсэн зохиолч: | |
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| Формат: | Recurso digital |
| Хэл сонгох: | |
| Хэвлэсэн: |
Zenodo
2025
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| Нөхцлүүд: | |
| Онлайн хандалт: | https://doi.org/10.5281/zenodo.17647706 |
| Шошгууд: |
Шошго нэмэх
Шошго байхгүй, Энэхүү баримтыг шошголох эхний хүн болох!
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Агуулга:
- <p>We report the discovery of a universal fixed point hierarchy in higher-dimensional geometric optimization. Analysis of dimensions 6D through 100D reveals that all dimensions share the same geometric exponent (2.020924) with zero error, producing a mathematical sequence of fixed points that converges to unity. We prove three fundamental theorems: (1) convergence of the fixed point sequence xD satisfying xD = x + 1 to xD = 1 + 1/(D − 1) + O(1/D2) → 1 as D → ∞ with explicit error bounds, (2) uniqueness of fixed points in each dimension, and (3) strict monotonicity of the sequence. We derive a closed-form generating function with 0.0068% accuracy and establish connections to the Padovan sequence and plastic constant. The fixed point hierarchy appears in all string theory dimensions (6D Calabi-Yau, 10D superstring, 11D M-theory, 26D bosonic), suggesting a geometric foundation for string compactifications. The plastic constant (1.324718) appears as a universal fixed point in every dimension, connecting crystal structures (3D), spacetime geometry (5D), and higher-dimensional physics. This work provides rigorous mathematical foundations for the unified geometric optimization principle discovered in ϕ-Geometry Paper V.</p>